ScalingStacks

Lemma 3.11. Let $W^{0}_{\pm}=W^{0}_{\pm}(\tau,o)$ and $W^{x}_{\pm}=W^{x}_{\pm}(\tau,o)$ be pairs of corresponding webs in $\left\llbracket L^{0}_{\pm}\right\rrbracket$ and $\left\llbracket L^{x}_{\pm}\right\rrbracket$ respectively. Further, let $s\in\{p,t\}^{2n}$ be a palindrome in which $t$ appears $2k$ times, and consider $W^{1}_{\pm}=W^{1}_{\pm}(\tau,o,s)$ and $W^{x-1}_{\pm}=W^{x-1}_{\pm}(\tau,o,s)$ in $\left\llbracket L^{1}_{\pm}\right\rrbracket$ and $\left\llbracket L^{x-1}_{\pm}\right\rrbracket$ respectively. Then

	$\displaystyle R2_{-}(W^{0}_{-},W^{1}_{-})$	$\displaystyle=(-1)^{k}R2_{+}(W^{0}_{+},W^{1}_{+})$
	$\displaystyle R2^{-1}_{+}(W^{x-1}_{+},W^{x}_{+})$	$\displaystyle=(-1)^{k}R2^{-1}_{-}(W^{x-1}_{-},W^{x}_{-}).$